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In this paper, we aim to study the asymptotic behavior (when    $$\varepsilon \;\rightarrow \; 0$$  ε → 0 ) of the solution of a quasilinear problem of the form    $$-\mathrm{{div}}\;(A^{\varepsilon }(\cdot ,u^{\varepsilon }) \nabla u^{\varepsilon })=f$$  - div ( A ε ( · , u ε ) ∇ u ε ) = f given in a perforated domain    $$\Omega \backslash T_{\varepsilon }$$  Ω \ T ε with a Neumann boundary condition on the holes    $$T_{\varepsilon }$$  T ε and a Dirichlet boundary condition on    $$\partial \Omega $$  ∂ Ω . We show that, if the holes are admissible in certain sense (without any periodicity condition) and if the family of matrices    $$(x,d)\mapsto A^{\varepsilon }(x,d)$$  ( x , d ) ↦ A ε ( x , d ) is uniformly coercive, uniformly bounded and uniformly equicontinuous in the real variable  d , the homogenization of the problem considered can be done in two steps. First, we fix the variable  d  and we homogenize the linear problem associated to    $$A^{\varepsilon }(\cdot ,d)$$  A ε ( · , d ) in the perforated domain. Once the    $$H^{0}$$  H 0 -limit    $$A^{0}(\cdot ,d)$$  A 0 ( · , d ) of the pair    $$(A^{\varepsilon },T^{\varepsilon })$$  ( A ε , T ε ) is determined, in the second step, we deduce that the solution    $$u^{\varepsilon }$$  u ε converges in some sense to the unique solution    $$u^{0}$$  u 0 in    $$H^{1}_{0}(\Omega )$$  H 0 1 ( Ω ) of the quasilinear equation    $$-\mathrm{{div}}\;(A^{0}(\cdot ,u^{0})\nabla u )=\chi ^{0}f$$  - div ( A 0 ( · , u 0 ) ∇ u ) = χ 0 f (where    $$ \chi ^{0}$$  χ 0 is    $$L^{\infty }$$  L ∞ weak    $$^{\star }$$  ⋆ limit of the characteristic function of the perforated domain). We complete our study by giving two applications, one to the classical periodic case and the second one to a non-periodic one.

H-convergence of a class of quasilinear equations in perforated domains beyond periodic setting